{
  "abstract": "We establish a connection between policy evaluation in Markov decision processes and PageRank in network analysis. For a fixed policy, we show that the value function of a discounted Markov decision process can be obtained, up to an explicit rescaling, from the PageRank vector of a suitably defined time-reversed Markov chain. In this correspondence, the discount factor plays the role of the teleportation parameter, while rewards induce the restart distribution. Beyond the irreducible case, invoking quasi-stationary distributions and Doob $h$-transforms, we prove a general decomposition theorem showing that policy evaluation for arbitrary finite MDPs reduces to a collection of PageRank problems on the recurrent and transient components of the policy-induced Markov chain. This framework naturally extends to undiscounted MDPs with terminal states and to transition-dependent rewards. We conclude by showing efficiency of our approach on a numerical example of a sticky random walk on large deterministic and random graphs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.00532",
  "author_total": 3,
  "authors": [
    {
      "name": "Konstantin Avrachenkov"
    },
    {
      "name": "Lorenzo Gregoris"
    },
    {
      "name": "Nelly Litvak"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5bw3ez2ws1m4w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.00532",
  "fulltext_url": null,
  "id": "5bw3ez2ws1m4w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.00532",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "1702|Reinforcement Learning in Robotics"
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  "openalex": "W7160197513",
  "pdf_url": "https://arxiv.org/pdf/2605.00532",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5bw3ez2ws1m4w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2605.00532",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.00532"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Linking PageRank, Time Reversal, and Policy Evaluation",
  "title_text": "Linking PageRank, Time Reversal, and Policy Evaluation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/5bw3ez2ws1m4w",
  "venue": "arXiv",
  "versions": []
}